Abstract: A boundary element method for obtaining the acoustic radiation characteristics under arbitrary boundary condition of axisymmetric structure is proposed. By using the improved Burton and Miller formulas, the hypersingular term is transformed into the sum of the weak singular terms to ensure the uniqueness of the acoustic radiation parameters and the calculation is simple and accurate. By expanding the surface velocity and pressure in Fourier series with respect to the angle of revolution and using the orthogonality of the series, the undetermined coefficient is established. The normalized operators of the Green function is translated into the tangential operators, which makes it easy to calculate the integrals directly. The surface integral formula is expressed as a line integral along the generator of the body and the integral over the circumferential angle. Furthermore, the relationship between the sound pressure and the vibration velocity is established with quadratic isoparametric elements to determine the acoustic radiation parameters. Taking a pulsating sphere and an oscillating sphere as examples, the results are compared with the analytical results and the results of the traditional boundary element method to illustrate the validity and accuracy of the method.